2,192 research outputs found
The Trial Brief
From the chapter Introduction: The object of the preceding chapters is to show the brief maker where to find the material for his brief, how to find it, and how to select out of the mass of material found that which will be suitable for his use.... The present purpose is to outline a course of investigation suitable to the preparation of a case for trial and to suggest methods of making the material collected during the search for authorities readily available. [p.417-418
An overview of Viscosity Solutions of Path-Dependent PDEs
This paper provides an overview of the recently developed notion of viscosity
solutions of path-dependent partial di erential equations. We start by a quick
review of the Crandall- Ishii notion of viscosity solutions, so as to motivate
the relevance of our de nition in the path-dependent case. We focus on the
wellposedness theory of such equations. In partic- ular, we provide a simple
presentation of the current existence and uniqueness arguments in the
semilinear case. We also review the stability property of this notion of
solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme
approximation method. Our results rely crucially on the theory of optimal
stopping under nonlinear expectation. In the dominated case, we provide a
self-contained presentation of all required results. The fully nonlinear case
is more involved and is addressed in [12]
A Corticothalamic Switch: Controlling the Thalamus with Dynamic Synapses
SummaryCorticothalamic neurons provide massive input to the thalamus. This top-down projection may allow the cortex to regulate sensory processing by modulating the excitability of thalamic cells. Layer 6 corticothalamic neurons monosynaptically excite thalamocortical cells, but also indirectly inhibit them by driving inhibitory cells of the thalamic reticular nucleus. Whether corticothalamic activity generally suppresses or excites the thalamus remains unclear. Here we show that the corticothalamic influence is dynamic, with the excitatory-inhibitory balance shifting in an activity-dependent fashion. During low-frequency activity, corticothalamic effects are mainly suppressive, whereas higher-frequency activity (even a short bout of gamma frequency oscillations) converts the corticothalamic influence to enhancement. The mechanism of this switching depends on distinct forms of short-term synaptic plasticity across multiple corticothalamic circuit components. Our results reveal an activity-dependent mechanism by which corticothalamic neurons can bidirectionally switch the excitability and sensory throughput of the thalamus, possibly to meet changing behavioral demands
Binomial coefficients, Catalan numbers and Lucas quotients
Let be an odd prime and let be integers with and . In this paper we determine
mod for ; for example,
where is the Jacobi symbol, and is the Lucas
sequence given by , and for
. As an application, we determine modulo for any integer , where denotes the
Catalan number . We also pose some related conjectures.Comment: 24 pages. Correct few typo
A differential method for bounding the ground state energy
For a wide class of Hamiltonians, a novel method to obtain lower and upper
bounds for the lowest energy is presented. Unlike perturbative or variational
techniques, this method does not involve the computation of any integral (a
normalisation factor or a matrix element). It just requires the determination
of the absolute minimum and maximum in the whole configuration space of the
local energy associated with a normalisable trial function (the calculation of
the norm is not needed). After a general introduction, the method is applied to
three non-integrable systems: the asymmetric annular billiard, the many-body
spinless Coulombian problem, the hydrogen atom in a constant and uniform
magnetic field. Being more sensitive than the variational methods to any local
perturbation of the trial function, this method can used to systematically
improve the energy bounds with a local skilled analysis; an algorithm relying
on this method can therefore be constructed and an explicit example for a
one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics
Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes
Recent theoretical work suggests that violation of the Equivalence Principle
might be revealed in a measurement of the fractional differential acceleration
between two test bodies -of different composition, falling in the
gravitational field of a source mass- if the measurement is made to the level
of or better. This being within the reach of ground based
experiments, gives them a new impetus. However, while slowly rotating torsion
balances in ground laboratories are close to reaching this level, only an
experiment performed in low orbit around the Earth is likely to provide a much
better accuracy.
We report on the progress made with the "Galileo Galilei on the Ground" (GGG)
experiment, which aims to compete with torsion balances using an instrument
design also capable of being converted into a much higher sensitivity space
test.
In the present and following paper (Part I and Part II), we demonstrate that
the dynamical response of the GGG differential accelerometer set into
supercritical rotation -in particular its normal modes (Part I) and rejection
of common mode effects (Part II)- can be predicted by means of a simple but
effective model that embodies all the relevant physics. Analytical solutions
are obtained under special limits, which provide the theoretical understanding.
A simulation environment is set up, obtaining quantitative agreement with the
available experimental data on the frequencies of the normal modes, and on the
whirling behavior. This is a needed and reliable tool for controlling and
separating perturbative effects from the expected signal, as well as for
planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan
16, 2006. 16 2-column pages, 9 figure
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Further improvements on TRACE 3-D
TRACE 3-D, an interactive beam-dynamics program that calculates the envelopes of a bunched beam (including linear space-charge forces) through a user-defined transport system, has undergone several upgrades in physics, coding, and capabilities. Recent modifications include centroid tracking (and misalignment capabilities) and an improved beam description that allows study of some nonlinear effects such as wakefields. The Fortran code has been made portable and runs on numerous platforms. It can be used with a variety of graphics packages. The additional beamline elements, new commands, expanded fitting capabilities, improved beam description, and coding modifications have extended TRACE 3-D`s usefulness and applicability to the accelerator community. These changes are documented in the third edition of TRACE 3-D Documentation
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio
We use a continuous version of the standard deviation premium principle for
pricing in incomplete equity markets by assuming that the investor issuing an
unhedgeable derivative security requires compensation for this risk in the form
of a pre-specified instantaneous Sharpe ratio. First, we apply our method to
price options on non-traded assets for which there is a traded asset that is
correlated to the non-traded asset. Our main contribution to this particular
problem is to show that our seller/buyer prices are the upper/lower good deal
bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko
(2006) and to determine the analytical properties of these prices. Second, we
apply our method to price options in the presence of stochastic volatility. Our
main contribution to this problem is to show that the instantaneous Sharpe
ratio, an integral ingredient in our methodology, is the negative of the market
price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar
(2000).Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe
ratio, correlated assets, stochastic volatility, non-linear partial
differential equations, good deal bound
Adaptive Markets and the New World Order
In the adaptive markets hypothesis (AMH) intelligent but fallible investors learn from and adapt to changing economic environments. This implies that markets are not always efficient but are usually competitive and adaptive, varying in their degree of efficiency as the environment and investor population change over time. The AMH has several implications, including the possibility of negative risk premiums, alpha converging to beta, and the importance of macro factors and risk budgeting in asset allocation policies
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